During a sale at h&m, you buy three sweatshirts and two pairs of pants for $85.50. Later in the day, your friend buys three
sweatshirts and four pairs of pants for $123. Define your variables and write a system of equations to represent the situation if you wanted to find out how much each item costs individually.
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<h2>Systems of Equations Word Problems</h2>
To solve these questions, we can translate key words into operations:
- <em>Difference</em> = subtract
- <em>Twice</em> = double
- <em>Less than</em> = subtract
We're given:
- Difference of Annie's age and twice Carl's age is 22
- Annie's age is 13 less than 3 times Carl's age
There are two variables given two us: Annie's age and Carl's age.
- Let Annie's age be equal to <em>x.</em>
- Let Carl's age be equal to <em>y</em>.
Translate the given information into two equations:
- Difference of Annie's age and twice Carl's age is 22
⇒
- Annie's age is 13 less than 3 times Carl's age
⇒
Now, we can substitute the fist equation into the second one to solve for <em>y</em>:
Now, substitute <em>y</em> back into the second equation to solve for <em>x</em>:
Therefore, Grandma Annie is 92 years old.